Oh, that's funny! And I'm sure almost everybody has some variant of that story. My husband is a take-charge type and can usually think what to do in a crisis, or a non-crisis - until, several years ago, I fell down the steps in our house and broke my ankle quite thoroughly. The kids (high-school age, who thought it was exciting, or at least interesting) got their dad, who took one look at my balloon of an ankle - and turned dead white. He almost threw up. It took a few minutes for him to be able to call 911.
The closest story I can tell on myself, I think, had to do with my fear of nasty insects. Not the regular bugs, like flies and ants - the scary ones like wasps and spiders. When I was little, I was even afraid to look at pictures of them because I thought they might come alive. I always let my parents or some other grownup go after the wasps in the attic or in the car WE were in, or the big spiders who showed up every summer. Then one day, after my husband and I had just moved into our first house, I saw a big ol' (gasp!) spider on the living room wall, and looked around for a grownup to take care of it. Guess what I realized.
Train your kids well to bring you water when you need it! Tell 'em you'll do the same for them some time.
On the more serious side, taking a course in first aid might help you learn to keep cooler in a crisis involving, um, that red stuff. At least maybe you wouldn't faint until it was all over.